List of supplementary files with explanations:
==============================================

General remarks:
----------------
* coding of unary operations
  We use integers to code unary operations appearing as elements of
  centralising monoids. If u ∈ OA⁽¹⁾ on A = {0,1,2,3} is given by its
  value table u∘(0,1,2,3) = (a,b,c,d), then we interpret "abcd" as the
  base-4-representation of an integer, namely of l = 64a + 16b + 4c + d.
  This number l = 4³u(0) + 4²u(1) + 4u(2)+ u(3) is used to denote u as
  an element of a transformation monoid on A = {0,1,2,3}. Every
  transformation monoid on A thus becomes a subset of {0,…,255}.

* representation of (other) operations
  Unary operations are either represented as
    - an integer l ∈ {0,…,255} as explained above
    - an integer l ∈ {0,…,255} with some prefix, such as "fl"
    - their value table abcd, possibly with a prefix
    - a line number in a file where the operations / their
      centralising monoids are listed
  Binary operations are usually represented by
    - a line number in a file where the operations / their
      centralising monoids are listed
    - a value table abcd|efgh|ijkl|mnop representing values g(x,y)
      g(x,y) | 0 1 2 3
      -------+--------
           0 | a b c d
           1 | e f g h
           2 | i j k l
           3 | m n o p
      where x-values correspond to rows and y-values to columns, e.g.,
      g(1,3) = h.

* Burmeister format for formal contexts
  a simple way to represent a formal context K = (G,M,I)
    - first line: letter "B"
    - second line: empty
    - third line: |G| number of objects
    - fourth line: |M| number of attributes
    - fifth line: empty
    - the following |G| lines: identifies for the objects
                               (rows of the context)
    - the following |M| lines: identifies for the attributes
                               (columns of the context)
    - the following |G| lines: the rows of the context;
                               echo row contains |M| characters "." or "X"
                               representing (g,m) ∉ I or (g,m) ∈ I


Files relating to Subsection 3.1:
---------------------------------
* contexts:
  K1.cxt
    the context K₁ = (OA⁽¹⁾,OA⁽¹⁾,⊥) in Burmeister format

* all concepts (plain and up to conjugacy):
  1485_concepts_witn_unary_ops.txt
    a list of all 1485 concepts of the context K₁ as pairs of a
    witnessing set F and of the respective centralising monoid F*⁽¹⁾

  1485_monoids_witn_unary_ops.txt
    a list of all 1485 centralising monoids that can be witnessed
    by unary operations, that is, the intents of the context K₁

  1485_monoids_witn_unary_ops_up_to_conj.txt
    a list of all 1485 centralising monoids that can be witnessed
    by unary operations, that is, the intents of the context K₁,
    categorised into 106 element-wise conjugacy classes of monoids,
    including the 106 representatives; the monoids referenced in this
    file can be found in 1485_monoids_witn_unary_ops.txt

* specific monoids
  256_monoids_witn_1_unary_op.txt
    a list of all 256 centralising monoids that can be witnessed by a
    single unary operation, that is, the object intents of K₁

  49_max_monoids_witn_1_unary_op.txt
    a list of all 49 unary operations witnessing centralising monoids
    that are co-atoms with respect to K₁, together with a classification
    of the describing unary function

* specific monoids up to conjugacy (of witnesses = of monoids)
  49_max_monoids_witn_1_unary_op_up_to_conj.txt
    a list of all 49 unary operations witnessing centralising monoids
    that are co-atoms with respect to K₁, categorised into 6
    conjugacy classes, including the 6 representatives


Files relating to Section 4:
----------------------------
* contexts:
  K2prime.cxt
    the context K₂' = (G,OA⁽¹⁾,⊥) in Burmeister format, which is an
    object clarified subcontext of K₂ = (CA*⁽²⁾,OA⁽¹⁾,⊥);
    K₂' describes the same lattice of intents (centralising monoids)
    as K₂;
    this is a large file as |G| = 10263;
    the objects from G can be found in the file
    10263_monoids_witn_1_binidemp_op.txt

  K2dagger.cxt
    the context K₂† = (̃G,OA⁽¹⁾,⊥) in Burmeister format, which is an
    object reduced subcontext of K₂'; |̃G| = 1236
    K₂† describes the same lattice of intents (centralising monoids)
    as K₂' and K₂.
    the 1236 functions in ̃G are listed in tables in the appendix A
    and in the file 1236_monoids_witn_1_binidemp_op.txt

* all concepts (plain and up to conjugacy):
  17013_concepts_witn_binidemp_ops.txt
    a list of all 17013 concepts of the context K₂ as pairs of a
    witnessing set F and of the respective centralising monoid F*⁽¹⁾

  17013_monoids_witn_binidemp_ops.txt
    a list of all 17013 centralising monoids that can be witnessed
    by binary idempotent operations, that is, the intents of the
    context K₂ / K₂' / K₂†

  17013_monoids_witn_binidemp_ops_up_to_conj.txt
    a list of all 17013 centralising monoids that can be witnessed
    by binary idempotent operations, that is, the intents of the
    context K₂, categorised into 923 element-wise conjugacy classes of
    monoids, including the 923 representatives;
    the monoids referenced in this file can be found in
    17013_monoids_witn_binidemp_ops.txt

* specific monoids
  10263_monoids_witn_1_binidemp_op.txt
    a list of all 10263 centralising monoids that can be witnessed by a
    single binary idempotent non-projection, that is, the object
    intents of K₂';
    the file includes a witnessing binary idempotent operation for each
    monoid

  1236_monoids_witn_1_binidemp_op.txt
    a list of all 1236 centralising monoids that can be witnessed by a
    single binary idempotent non-projection from ̃G, that is, the object
    intents of K₂†;
    the file includes a witnessing binary idempotent operation for each
    monoid and the size of the monoid in []

  612_max_monoids_witn_1_binidemp_op.txt
    a list of all 612 binary idempotent operations witnessing
    centralising monoids that are co-atoms with respect to K₂;
    the list includes the witnesses, the monoids and a number (l) where
    1 ≤ l ≤ 10263 is the line number of the witness in the file
    10263_monoids_witn_1_binidemp_op.txt

* specific monoids up to conjugacy of witnesses
  10263_monoids_witn_1_binidemp_op_up_to_wconj.txt
    a list of all 10263 binary idempotent non-projections in the object
    set G of K₂',
    categorised into 2274 conjugacy classes of witnesses with
    representatives given at the end;
    the witnesses and monoids referenced by integers in this file can
    be found in the respective line of
    10263_monoids_witn_1_binidemp_op.txt

  1236_monoids_witn_1_binidemp_op_up_to_wconj.txt
    a list of all 1236 binary idempotent non-projections in the object
    set ̃G of K₂†,
    categorised into 142 conjugacy classes of witnesses with
    representatives given at the end;
    the witnesses and monoids referenced by integers in this file can
    be found in the respective line of
    1236_monoids_witn_1_binidemp_op.txt

  612_max_monoids_witn_1_binidemp_op_up_to_wconj.txt
    a list of all 612 binary idempotent operations witnessing
    centralising monoids that are co-atoms with respect to K₂' / K₂†,
    categorised into 77 conjugacy classes of witnesses with
    representatives given at the end;
    the witnesses and monoids referenced by integers in this file can
    be found in the respective line of
    1236_monoids_witn_1_binidemp_op.txt

* specific monoids up to conjugacy of monoids
  10263_monoids_witn_1_binidemp_op_up_to_conj.txt
    a list of all 10263 centralising monoids that can be witnessed
    by a single binary idempotent non-projection (object intents of K₂'),
    categorised into 563 element-wise conjugacy classes of monoids with
    representatives given at the end;
    the witnesses and monoids referenced by integers in this file can
    be found in the respective line of
    10263_monoids_witn_1_binidemp_op.txt

  1236_monoids_witn_1_binidemp_op_up_to_conj.txt
    a list of all 1236 centralising monoids that can be witnessed by a
    single binary idempotent non-projection from ̃G, that is, the object
    intents of K₂†,
    categorised into 83 element-wise conjugacy classes of monoids with
    representatives given at the end;
    the witnesses and monoids referenced by integers in this file can
    be found in the respective line of
    1236_monoids_witn_1_binidemp_op.txt

  612_max_monoids_witn_1_binidemp_op_up_to_conj.txt
    a list of all 612 centralising monoids that are co-atoms with
    respect to K₂' / K₂†
    categorised into 42 element-wise conjugacy classes of monoids with
    representatives given at the end;
    the witnesses and monoids referenced by integers in this file can
    be found in the respective line of
    1236_monoids_witn_1_binidemp_op.txt
